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Proofs That Really Count: the Art of Combinatorial Proof is an undergraduate-level mathematics book on combinatorial proofs of mathematical identies.That is, it concerns equations between two integer-valued formulas, shown to be equal either by showing that both sides of the equation count the same type of mathematical objects, or by finding a one-to-one correspondence between the different ...
The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something about everyday life, or when data used in an argument is numerical. It is sometimes also used to mean a "statistical proof" (below), especially when used to argue from data.
Proofs from THE BOOK is a book of mathematical proofs by Martin Aigner and Günter M. Ziegler. The book is dedicated to the mathematician Paul Erdős, who often referred to "The Book" in which God keeps the most elegant proof of each mathematical theorem. During a lecture in 1985, Erdős said, "You don't have to believe in God, but you should ...
The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
99 Variations on a Proof is a mathematics book by Philip Ording, in which he proves the same result in 99 different ways. Ording takes an example of a cubic equation , x 3 − 6 x 2 + 11 x − 6 = 2 x − 2 , {\displaystyle x^{3}-6x^{2}+11x-6=2x-2,} and shows that its solutions are x = 1 {\displaystyle x=1} and x = 4 {\displaystyle x=4} using a ...
The onset of this phase typically occurs during a 'transition to higher mathematics' course, an 'introduction to proofs' course or an introductory course in mathematical analysis or abstract algebra. Students of computer science or applied mathematics may encounter this formalism during their underclassman undergraduate years via a course in ...